Download Newton`s Laws of Motion

Newton’s Laws of Motion
Chapter 4
Changes in Motion
Section 4.1
• Force is simply a push or pull
• It is an interaction between two or more objects
• Force is a vector so it has magnitude and
direction
• In the SI system, Force is measured in Newtons
(N). In the English system, it is measured in
pounds.
• 1 pound = 4.445 Newtons
• The total force (or net force) exerted on an object
is the vector sum of all forces acting on it
Aristotle & Galileo
• Aristotle was a great
philosopher but not
such a good scientist.
• Aristotle’s theory of
motion is wrong.
• Took 2000 years before
Galileo got motion right.
Motion according to Aristotle (I)
• Every object has a “natural” state.
• In “natural motion”, “Earth” elements
(stone, apple, you, etc.) are drawn to
the Earth.
• Heavier objects are more strongly
attracted so they fall faster (stone
falls faster than a feather).
Aristotle
Important: These are Aristotle’s ideas, but he’s wrong!
Reality
Motion according to Aristotle (II)
• Pushing or pulling an object causes
“unnatural” motion (or “violent”
motion).
• If cause is removed (stop pushing) then
object returns to “natural” state and
stops moving.
Pushed brick slides but then comes to a stop
BRICK
BRICK
Galileo’s Inclines (I)
Downhill: Speed increases
Uphill: Speed decreases
Flat surface: Speed increases, decreases,
or constant?
Questions existence of “natural Earth” state of not moving.
Inertia
section 4.2
• An object’s tendency to persist in its original
state of motion
• This concept was first discovered by Galileo in
the 1630’s.
• Objects will keep doing whatever they’re
already doing unless something causes it to
change.
Isaac Newton
• 1642-1727, Lincolnshire, England
• Professor and Scholar at the
University of Cambridge
• One of the most influential
scientists of all time
• Uncovered universal laws of
motion and gravity among many
other discoveries.
• Most famous work: Principia
Newton’s First Law of Motion
also referred to as the “law of inertia”
An object at rest remains at rest & an
object in motion remains in motion*,
unless an outside, unbalanced force acts
on the object.
*Moving in a straight line with constant speed.
Newton’s First Law of Motion
• An object in motion can still maintain
its state with a force acting on it.
• It’s only when the forces acting on it
are unbalanced that an object can
change its motion!
Newton’s First Law of Motion
• The Gare Montparnasse
in France crashed
through this wall in 1895,
why?
• Trains are difficult to stop
because they are so
massive
• There is a direct
relationship between
mass and inertia.
Mass
• Mass is a measure of the quantity of
matter in an object
• Mass also measures how difficult it is to
change the velocity of an object
• Or, how much an object resists changes in
its motion
Example: Riding the subway
When a moving train
stops, you continue
moving forward.
When the stopped
train starts moving
again, you remain
stationary and are
thrown backwards
Question
When the rocket engines on a spacecraft are suddenly
turned off, while traveling in empty space far away from
distant stars and planets, the starship will..
A) go faster and faster
B) slow down and then stop
C)stop immediately
D)move with constant speed
E) move perpendicular to velocity
Inertia demonstrations
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•
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Coin/notecard
Tablecloth
Hanging mass
Hoop and battery
Mallet and mass
Rolling carts
Discussion topics of inertia
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Inertia videos
Getting ketchup out
When are you taller? AM or PM?
Collisions: Front and rear
Seatbelts work off inertia
If you drop something on a moving vehicle, where
does it land?
• How do you find your mass in space?
Conceptual Checkpoint
• The metal head of a hammer is loose. To
tighten it, you drop the hammer down onto
a table. Should you (a) drop the hammer
with the handle end down, (b) drop the
hammer with the head end down, or (c) do
you get the same result either way?
Conceptual Checkpoint
Tighten the Hammer Head
Net Force ( ∑ F)
When several forces act on an object, the forces
add together.
Sum of forces called net force or total force
3 Newtons
5 Newtons
8 Newtons
BRICK
same as
The Newton is metric unit of force (about 1/5 pound).
Check Yourself
?
Equilibrium Rule
If an object is at rest then the net force must be
zero. Similarly if in uniform motion.
Zero Newtons
(No Force)
3 Newtons
3 Newtons
BRICK
same as
When this happens we say that forces “balance.”
What is. . .
• Mass
• Weight, w
Weight vs Mass
• Mass is the amount of matter in an object
• Weight is a measure of the pull of gravity on an
object.
•
Weight (Newtons) = mass (kg) x acceleration due to gravity (m/s2)
• Formula for weight: W = m g
• Q: How much does one kilogram weigh?
• A: 9.8 N
Question
Is it better to have 1 N of gold on the moon or
on the Earth?
Example
An astronaut with a mass of 75 kg
travels to Mars.
A) What is his mass on Mars?
B) What is his weight on Mars
where the acceleration due to
gravity is 3.8 m/sec2?
C) What is the acceleration due
to gravity on top of a mountain if
he weighs 683 N?
Free Body Diagrams
• A free body diagram is a diagram showing
an object in free space along with all
external forces acting on it
Free Body Diagrams
• The usual steps in constructing a freebody diagram are:
– Sketch the forces
– Isolate the object of interest
– Choose a convenient coordinate system
– Resolve the forces into components
• You can then apply Newton’s 2nd law for
each coordinate direction
Constructing and Using a Free-Body Diagram
Figure 5-5bc
Constructing and Using a Free-Body Diagram
Constructing and Using a Free-Body Diagram
A Book Supported in a Person’s Hand
Example
Find the magnitude and direction of the net
force.
23N
45 N
Example
Find the magnitude and direction of the net
force.
15 N
13 N
24 N
Example
Four forces act on an object. 210 N acts to the
East. 305 N acts to the South. 413 N acts to
the West. And, 139 N acts to the North. Find
the magnitude and direction of the net force.
Example
Three forces act on an object. 71 N act at 24
degrees North of East. 62 N act at 51 degrees
North of West. And, 85 N act at 60 degrees
South of West. Find the magnitude and
direction of the net force.
Example
• The following object is in equilibrium. How
big does the missing force have to be to keep
it in equilibrium?
F= ?
16 N
16 N
11 N
Example
• Find the size and direction of the missing
force in order for this object to be in
equilibrium.
3.3 N
F=?
6.3 N
Example
• Find the size and direction of the missing
force in order for this object to be in
equilibrium.
33 N at 60 degrees N of E
63 N at 15 degrees S of E
F=?
Example
• This 1kg mass is suspended by two cables at 50
degrees. Find the size and direction of the
tension force in each cable in order for this object
to be in equilibrium.
T=?
T=?
50°
50°
1 kg
Newton’s 2nd Law
Section 4.3
• When a net force acts on an object of mass m,
the acceleration of the object will be given by:
Σ𝐹 = 𝑚𝑎
• Or in terms of components:
Fx  max
Fy  ma y
Newton’s 2nd Law
• If the net force is zero, the acceleration is
zero, and the velocity of an object stays
constant, which is Newton’s 1st law
• Force is measured in newtons (N), and
from the second law,
1 N  1 kg  m/s
2
Newton’s Second Law of Motion
• Fnet = ma
4.45 N = 1 lb
Example
What is the net force required
to accelerate a 1.5 kg box at 2.0
m/sec2?
Example
What is the net force exerted on
a 1500 kg car if it is accelerated
from 5 m/sec to 10 m/sec in 3
sec?
Example
• A 0.34 kg softball is accelerated from rest
to 22 m/s over a length of 0.88 meters.
Find the net force that was applied to the
ball that produced this acceleration.
Example
• The following forces act on the 4.6 kg
object. A) Find the net force acting on it.
B) Find the magnitude of its acceleration.
15 N
13 N
24 N
4N
Example
• Find the acceleration of the apparatus
below. Assume there is no friction.
3.3 kg
0.75
kg
Example
• A 2,360 kg pickup truck slows down to a
complete stop with a frictional force of
14,500 N directed opposite its motion. If
its initial velocity was + 14.2 m/s, how far
did it travel while slowing down? How
much time did this take?
Newton’s 3rd Law
Newton’s 3rd Law
• For every force that acts on an object,
there is a reaction force equal in
magnitude and opposite in direction.
• For every action there is an equal and
opposite reaction.
• An isolated force does not exist in nature,
so forces always occur in pairs
Newton’s 3rd Law
• Action−reaction forces act on two different
objects: hence they do not cancel
• Action−reaction forces generally produce
different accelerations, since the masses
of the objects are likely to be different
Examples of Action-Reaction Force Pairs
Apparent Weight
• When you are in an elevator accelerating
upward a scale would read a greater weight
• When you are in an elevator accelerating
downward a scale would read a lesser
weight
• Thus, your apparent weight in an
accelerator is different from your true weight
Apparent Weight
Apparent Weight
• If you are accelerating upward, your
apparent weight is
Wa  m( g  a)
• If you are accelerating downward, your
apparent weight is
Wa  m( g  a)
Normal Forces
• When an object rests on a surface, the
surface provides a force on the object in a
direction perpendicular to the surface
• This called the normal force, N
• In most cases, the normal force is equal to
the weight of the object; however it can be
greater or less than the weight of the
object
Support (Normal) Force
Solid surfaces exert a force, called a support
force, on objects pressed against them.
100 Newton
Gold Brick
100 Newton
Support force
(Normal Force)
* The term “normal” means
“perpendicular”. So the normal force is
always perpendicular to the surfaces
Downward force (weight)
balanced by upward force
(support).
The Normal Force
May Equal the Weight
Normal Forces
• When a box is pulled by a force F at an
angle θ across a smooth floor, the
magnitude of the normal force is
N  W  F sin 
The Normal Force
May Differ from the
Weight in certain
circumstances
Normal Forces
• For an inclined plane, the normal forces
are still at right angles to the surface, but
not in the vertical direction
• It is convenient to choose the x axis
parallel to the incline surface and y axis
perpendicular
• Then normal force is:
N  W cos
Components of the Weight on an Inclined
Surface
Example
• A child of mass 45 kg rides on a sled down an
ice-covered hill (frictionless) inclined at an
angle of 22 degrees with respect to the
horizontal.
• A) What is the acceleration of the child?
• B) What is the normal force exerted on the child by the
sled?
• Driving down the road you hit the brakes
suddenly. As a result, your body moves
toward the front of the car. Explain, using
Newton’s laws.
• A drag-racing car accelerates forward
because of the force exerted on it by the
road. Why, then, does it need an engine?
Explain.
• An astronaut on a space walk discovers
that his jet pack no longer works, leaving
him stranded 50 m from the spacecraft. If
the jet pack is removable, explain how the
astronaut can still use it to return to the
ship.
• Is it possible for an object to be in motion
and yet have zero net force acting on it?
Explain.
• You are dribbling a basketball, ready to
make your move to the hoop. What
produces the force that causes the ball to
return to your hand with each dribble?
• You jump out of an airplane and open your
parachute after a brief period of free fall.
To decelerate your fall, must the force
exerted on you by the parachute be less
than, equal to, or greater than your
weight? Explain.
• Is it possible for an object at rest to have
only a single force acting on it? If your
answer is yes, provide an example. If your
answer is no, explain why not.
• Since all objects are “weightless” for an
astronaut in orbit, is it possible for
astronauts to tell whether an object is
heavy or light? Explain.
Everyday Forces
Section 4.4
Two types of Friction
•Static
•Kinetic
Friction
• Friction is the force that opposes motion
when two surfaces are in contact
• Opposes motion means that the force of
friction is always in the opposite direction of
the motion
• There are two different types of friction: static
and kinetic (sliding)
Static Friction
• Static means stationary or not moving
• When a force is first applied to an object,
static friction opposes the start of motion
• A force greater than that of static friction must
be applied for the object to start moving
Kinetic Friction
• Kinetic means related to motion
• Kinetic friction opposes motion once an object
is moving
• Kinetic friction in general is less than static
friction
• This means you have to push harder to start
an object moving than to keep an object
moving
What Affects Friction?
• Speed of pull? (assuming v>0)
• Area in contact?
• Weight of object?
• Materials in contact?
Ff = FN
s > k
 is the coefficient of friction
What if . . . ?
• FA < Ff
• FA = Ff
• FA > Ff
• Ff is NOT an “applied” force!!
Question
It's more difficult to start moving a heavy carton from
rest than it is to keep pushing it with constant
velocity, because
A) the normal force (N) is greater when the carton is
at rest.
B) s< k
C) initially, the normal force (N) is not perpendicular
to the applied force.
D) k < s
Example
• A 13.4 kg crate is pushed across a floor.
The respective coefficients of friction are
µs = 0.85 and µk = 0.62. Find the pushing
force necessary to get it moving from rest.
And, find the force necessary to keep it
moving at a constant velocity.
13.4 kg